Hausdorff dimension and Perron-Frobenius theory

C Eigenfunctions of Perron-frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius op...

Perron-frobenius Theory for Complex Matrices

The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Agai...

C Eigenfunctions of Perron-frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Complex Continued Fractions

In a previous paper [11], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications in one dimension. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators ...

C Eigenfunctions of Perron-frobenius Operators and a New Approach to Numerical Computation of Hausdorff Dimension: Applications in R

We develop a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In the one dimensional case that we consider here, our methods require only C3 regularity of the maps in the IFS. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linea...

Weighted Frobenius-Perron and Koopman operators